 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/ii/paper-3/9b/b/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

\dot{ϕ}

gives

\overset{ρ}{˙} = - 3 H \dot{ϕ}^{2} .

Comparison with

\overset{ρ}{˙} + 3 H (ρ + P) = 0

yields

ρ + P = \dot{ϕ}^{2}

, and therefore

P = \frac{1}{2} \dot{ϕ}^{2} - V (ϕ) .

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